## The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh and Twelfth ; the Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored ; Also the Book of Euclid's Data, in Like Manner Corrected |

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Resultat 1-5 av 6

Side 30

For , if it be not greater , it must either be equal to it , or less ; but the

not equal to the angle EDF , because then the base BC would be equal ( 4. 1. ) to

EF ; but it is not ; A D therefore the

For , if it be not greater , it must either be equal to it , or less ; but the

**angle BAC**isnot equal to the angle EDF , because then the base BC would be equal ( 4. 1. ) to

EF ; but it is not ; A D therefore the

**angle BAC**is not equal to the angle EDF ... Side 91

1 In a circle , the angle in a semicircle is a right angle ; but the angle in a segment

greater than a semicircle is less than a right ... to the two angles ABC , ACB ;

therefore the

1 In a circle , the angle in a semicircle is a right angle ; but the angle in a segment

greater than a semicircle is less than a right ... to the two angles ABC , ACB ;

therefore the

**angle BAC**is equal to the angle FAC , and each of them is there . Side 189

to DCE : therefore the angle ABC is equal to the angle DCE ; and the

was proved to be equal to ACD : therefore the whole angle ACE is equal to the

two angles ABC , BAC ; add the common angle ACB , then the angles ACE , ACB

...

to DCE : therefore the angle ABC is equal to the angle DCE ; and the

**angle BAC**was proved to be equal to ACD : therefore the whole angle ACE is equal to the

two angles ABC , BAC ; add the common angle ACB , then the angles ACE , ACB

...

Side 211

If a solid angle be contained by three plane angles , any two of them are greater

than the third . * Let the solid angle at A be contained by the three plane

If a solid angle be contained by three plane angles , any two of them are greater

than the third . * Let the solid angle at A be contained by the three plane

**angles**,**BAC**, CAD , DAB . Any two of them are greater than the third . If the**angles BAC**... Side 431

similar to OPQ : because , as has been shown , the ratio of AD to BC is the same

with the ratio of ( HF to FL , that is , by the construction , with the ratio of ) OR to

PQ ; and the

...

similar to OPQ : because , as has been shown , the ratio of AD to BC is the same

with the ratio of ( HF to FL , that is , by the construction , with the ratio of ) OR to

PQ ; and the

**angle BAC**is equal to the angle POQ ; therefore the triangle ABC is...

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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid,Robert Simson Uten tilgangsbegrensning - 1825 |

The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Euclid,Robert Simson Uten tilgangsbegrensning - 1838 |

### Vanlige uttrykk og setninger

added altitude angle ABC angle BAC base centre circle circle ABCD circumference common cone cylinder definition demonstrated described diameter divided double draw drawn equal equal angles equiangular equimultiples Euclid excess fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise magnitude manner meet multiple Note opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition pyramid Q. E. D. PROP radius reason rectangle rectangle contained rectilineal figure remaining right angles segment shown sides similar sine solid solid angle sphere square square of AC taken THEOR third triangle ABC wherefore whole

### Populære avsnitt

Side 9 - Let it be granted that a straight line may be drawn from any one point to any other point.

Side 81 - The angles in the same segment of a circle are equal to one another.

Side 315 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.

Side 33 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 49 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.

Side 96 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.

Side 155 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Side 22 - ANY two angles of a triangle are together less than two right angles.

Side 25 - Let A, B, C be the three given straight lines, of which any two whatever are greater than the third, viz.

Side 24 - Any two sides of a triangle are together greater than the third side.